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If set S consists of the numbers 1,5,-2,8 and n, is 0 < n < 7?

(1) The median of the numbers in S is less than 5 (2) The median of the numbers in S is greater than 5

The software says the correct answer is C. I thought it would be A. I can't figure out why we need (2) to determine the answer.

Thanks, arl

n can be 1,2,3,4,5,6 1: Not enough if median is less than 5, then n can be any value less than 5 so n<5 even negative so the condition 0<n<7 is not hold fully. 2: Not enough if median is more than 5, then n can be any value more than 5 so n>5 even more than 7. I dont think you the choices can be combined.

If set S consists of the numbers 1,5,-2,8 and n, is 0 < n < 7?

(1) The median of the numbers in S is less than 5 (2) The median of the numbers in S is greater than 5

The software says the correct answer is C. I thought it would be A. I can't figure out why we need (2) to determine the answer.

Thanks, arl

stmt 2 doesn't sound right. Are you sure it's accurate. If the series is 1,5,2,-8,n whatever n value might be median can't be greater than 5. Since there are 5 elements the 3rd element in the ascending order should be the median.

If n <1 median =1 If 1<n<5 median =n If n>5 median =5
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Can someone please give an explanation for this question? Thanks.

Firs of all statement (2) should read: The median of the numbers in S is greater than 1.

If set S consists of the numbers 1, 5,-2, 8 and n, is 0 < n < 7?

Note that: If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order; If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

So the median of our set of 5 numbers: {-2, 1, 5, 8, n} must be the middle number, so it can be: 1 if \(n\leq{1}\); 5 if \(n\geq{5}\); \(n\) itself if \(1\leq{n}\leq{5}\).

(1) The median of the numbers in S is less than 5 --> so either the median=1 and in this case \(n\leq{1}\) so not necessarily in the range \(0<n<7\) or median=n and in this case \(1\leq{n}<{5}\) and in this case \(0<n<7\) is always true. Not sufficient.

(2) The median of the numbers in S is greater than 1 --> again either the median=5 and in this case \(n\geq{5}\) so not necessarily in the range \(0<n<7\) or median=n and in this case \(1<{n}\leq{5}\) and in this case \(0<n<7\) is always true. Not sufficient.

(1)+(2) \(1<median<5\) --> \(median=n\) --> \(1<n<5\), so \(0<n<7\) is true. Sufficient.

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